• Market supply
• Competitive equilibrium
• Total surplus and efficiency
• Taxes and subsidies
• Price maintenance
• Application: Imports
Competitive Markets
Three fundamental characteristics
1) Price taking behaviour: No buyer or seller is able to influence the market price.
2) Homogeneous products: The goods offered by the sellers are perfectly identical.
3) Free entry: Sellers can enter or exit the market freely.
Example: The market for carrots
1) Price taking behaviour: The large number of buyers and sellers of carrots implies that the behaviour of one of them cannot influence the market price.
2) Homogeneous produtcs: The carrots of one producer are more or less identical to the carrots of another
producer.
3) Free entry: Everybody can sell the carrots which grow in his garden.
From firm supply to market supply
• The market supply curve relates the total output of a market and the market price
• We have to distinguish between the short run and the long run. In the long run firms can enter or exit the market. In the short run the number of firms in the market is constant.
• To calculate market supply in the short run we can simply add individual firms' supplies at any given price.
S3
Short run market supply with three firms
P
0
S1
Q S2
P1 P2 P3
S3
P S1
SS
The short run aggregate supply curve is the
horizontal sum of the individual firms' supply curves.
Q S2
P1 P3
P2
Short run market supply with three firms
• In the long run firms can enter and exit the market. Every firm that could obtain positive profits will enter the market. Every firm that obtains negative profits will exit.
• We suppose that all firms are identical
• Firm supply: q*(p) Market supply: Q*(p)
• Let p* denote the minimum of LAC.
Long run market supply
(homogeneous firms)
LMC
LAC
If the market price is larger than p*
a firm which participates in the market makes positive profits. All firms strictly prefer to
enter the market. Market supply is infinite.
q1 q p*
p1 π > 0
p > p*: S(p) = ∞
p
Long run market supply
LMC
LAC
If the market price is smaller than p*
a firm which participates in the market makes negative profits. All firms strictly prefer to exit the market. The market supply is zero.
q2 q p*
p2 π < 0 p < p*: S(p) = 0
p
Long run market supply
LMC LAC
q* q
p*
p
p = p*: S(p) = nq*
n = 0,1,...∞
If the market price is equal to p*a firm which
participates in the market makes zero (economic)
profits. Firms are indifferent between participating in the market or not. Market supply is indeterminate.
Long run market supply
Long run market supply is a horizontal line where price is equal to the minimum of long run average cost.
LAC LMC
q p*
p
S(p)
Constant cost industry (LAC independent of Q)
Q
Firm p Industry
Long run market supply
p1
Increasing cost industry p2
Suppose that factor prices increase with the total factor demand of the industry. A higher aggregate output then
implies a higher LAC. The price at which firms are willing to produce increases with the total output of the industry.
LAC1
q
v
p
S(p)
Q
Firm p Industry
LAC2
Q2 Q1
Long run market supply
Market supply
- short run versus long run -
• The short run market supply slopes upwards when firms have increasing marginal costs (decreasing returns of the variable factors)
• The short run market supply can therefore have positive slope even if factor prices are constant.
• Long run market supply is horizontal when firms are identical and factor prices are constant.
• A positive slope of the long run market supply is caused by a positive correlation between factor prices and industry
output.
The elasticity of supply
The price- elasticity of supply measures the percentage change in supply as a
result of a one percent increase in price.
P/P E
PQ/Q
∆
= ∆
Perfectly elastic supply
P* S
Q P
E
P= ∞
The industry is willing to offer any quantity at a given price P*.
Short run: SMC is constant and equal to P* for each firm.
Long run: Factor prices are constant, firms are
homogeneous and the minimum of LAC is equal to P*.
Perfectly inelastic supply
Q* Q
P Price variations do not influence
the total quantitity supplied.
Example: Suppose that an
industry produces at capacity. In order to produce more the
industry would have to build more plants. A price increase would
then leave aggregate output unchanged in the short run.
E
P= 0
• Market supply
• Competitive equilibrium
• Total surplus and efficiency
• Taxes and subsidies
• Price maintenance
• Application: Imports
Competitive Markets
Competitive equilibrium
• In the chapter on Consumer Theory we have derived market demand D(P).
• In the chapter on Producer Theory we have derived the firms' cost functions
• Now we combine these two models in order to calculate a market equilibrium under perfect
competition.
PP**
QQ**
The principle of market clearing
P
Q Supply Supply
Demand Shortage
Surplus P1
P2
In equilibrium:
D(p*) = S(p*)
1. Each firm maximixes profits MCn(qn*) = p*
2. Aggregate supply equals market demand Q* = Σqn* = S(p*) = D(p*)
Short run competitive equilibrium
In the short run the number of firms in the market N is constant. A competitive equilibrium (p*, q1*,...,qN*) satisfies:
Short run competitive equilibrium
1. Individual firm supply Sn(p): SMCn with positive slope above SAVCn.
2. Market supply S(p) = ΣSn(p)
3. Equilibrium price and aggregate production:
D(P*) = S(P*) → P*, Q*
4. Individual output: SMCn(qn*) = P* → qn* A competitive equilibrium can be derived as follows:
S3 P
S1 q
S2 S3 P
SS
q
P SS
Q
P SS
Q DD p*
q3* Q*
Short run competitive equilibrium
S2 S1
q2* q1*
1.
3. 4.
2.
Firms Industry
Industry
Firms
Observations
• The equilibrium price p* is larger than the
minimum of SAVC. Thus, p* might be larger or smaller than SATC(q*).
• The three firms might have positive or negative profits.
• Therefore some firms might enter or exit the market in the long run.
• A short run equilibrium does not have to be an equilibrium in the long run.
Example
• Two firms with short run costs: C1=A+2q2; C2=A+5q2.
• Demand D(P) = 10 - (13/20)P.
Calculate the competitive equilibrium in the short run, (P*, q1*, q2*). Calculate the firms' profits in equilibrium.
Example
1. MC1 = 4q > AVC1 = 2q MC2 = 10q > AVC2 = 5q MC = P → S1(P) = P/4; S2(P) = P/10
2. S(P) = S1(P) + S2(P) = (7/20)P
3. D(P*) = S(P*) → P* = 10, Q* = 3.5 4. q1* = S1(P*) = 2.5; q2* = S2(P*) = 1
Profits: π1 = (25/2)-A; π2 = 5-A. Whether firms' make positive or negative profits depends on the parameter A.
Finish Lecture 11
1. Each firm maximizes profits and profits are zero:
LMC(q*) = p* = LAC(q*) 2. Aggregate supply = Demand:
Q* = N* q* = S(p*) = D(p*)
Long run competitive equilibrium (homogeneous firms)
In the long run firms will enter the market if there are positive profits and exit if profits are negative. The number of firms in the market is part of a long run equilibrium (p*, q*, N*).
Every long run equilibrium is also a short run equilibrium with N=N* firms.
Long run competitive equilibrium
1. Every firm maximizes profits and chooses output such that LMC = LAC → q(Q).
2. Zero profits: P = LAC(q(Q)). The inverse gives the market supply → S(P).
3. Equilibrium price and aggregate output:
D(P*) = S(P*) → P*, Q*
4. Individual firm output: q* = q(Q*)
5. Equilibrium number of firms: N* = Q*/q*
A long run equilibrium can be derived as follows:
Competitive equilibrium (increasing cost)
1. 2.
Q
p*
S(p) P Increasing cost
industry
Q*
LACQ1
q C
p(Q1)
S(p) p increasing cost
industry
q(Q1) Q
LACQ2
q(Q2)
p(Q2)
Q2 Q1
LACQ*
q C
q*
3. 4.
Example (increasing cost industry)
• Homogeneous firms with cost C(0) = 0 and C(q) = 16 + Bq2.
• Increasing cost industry B = B(Q) = 4Q2.
• Demand D(P) = 32 - (7/16)P
Calculate the long run equilibrium (p*, q*, N*).
Example (increasing cost industry)
1. MC = 2Bq; AC = 16/q + Bq MC = AC → q(Q) = 2/Q
2. P = AC(q(Q)) → P = 16Q
→ S(P) = P/16
3. D(P*) = S(P*) → P* = 64; Q* = 4 4. q* = q(Q*) = 0.5
5. N* = Q*/q* = 8
Competitive equilibrium (constant cost)
1. 2.
Q
p* S(p)
P Constant cost industry
Q*
LAC
q C Firm
p*
S(p) p Constant cost
industry
q* Q
3.
Example (constant cost industry)
• Homogeneous firms with cost C(0) = 0 and C(q) = 16 + Bq2.
• Constant cost industry: B = 16.
• Demand D(P) = 32 - (7/16)P
Calculate the long run equilibrium (p*, q*, N*).
Example (constant cost industry)
1. MC = 32q; AC = 16/q + 16q MC = AC → q(Q) = 1
2. P = AC(q(Q)) → S(P) = horizontal 3. D(P*)=S(P*) → P* = 32, Q* = 18 4. q* = 1 (independent of Q)
5. N* = Q*/q* = 18
Long run competitive equilibrium (heterogeneous firms)
Consider the market for gold. Gold mines differ in costs. Suppose there are 4 'good' mines and a large number of bad mines.
good mines
q
v
p
S(p)
Q p
bad mines
4q'b 4qb
qm qb q'b pm
pb
D(p)
Observations
• The long run aggregate supply can slope upwards even if factor prices are independent of industry output.
• 'Good' firms obtain positive profits even in the long run.
• 'Bad' firms obtain zero profits in the long run.
Economic rents
The good mines obtain positive profits because gold is found easily on their territory. The 'good territory' gives them an
economic rent. A bad mine would be willing to pay an amount equal to the good mines profits in order to obtain a good
territory.
good mines
q
v
p
S(p)
Q p
bad mines
4q'b 4qb
qm qb q'b pm
pb
D(p)
π > 0
Economic rents
• The economic rent of a factor of production is the difference between the amount firms' would be willing to pay for the factor and the minimum amount necessary obtain the factor.
• A markets producer surplus is the sum of the
economic rents of all factors which are necessary for production.
• In a competitive market producer surplus might be positive even if all firms make zero profits. In this case the economic rents are obtained by the
providers of the factors of production.
• Market supply
• Competitive equilibrium
• Total surplus and efficiency
• Taxes and subsidies
• Price maintenance
• Application: Imports
Competitive Markets
Total surplus in a competitive market
• Measure of the benefits which buyers and sellers have from participating in the
market.
• Sum of consumer and producer surplus.
• Consumer surplus = Buyers' willingness to pay - price paid (Area below the demand curve and above the price).
• Producer surplus = Price received by seller - cost of production (Area below the price and above the supply curve).
Consumer and producer surplus
Producer surplus
Consumer surplus
Producer and consumer suplus of a competitive market
Q P
S
D Q*
P*
• Total surplus = Consumer surplus + Producer surplus
• Consumer surplus = Willingness to pay - PB (PB =price payed by buyers)
• Producer surplus = PS - Sellers' costs (PS = price received by sellers)
• If there are no taxes nor subsidies: PB = PS
• Total surplus = Willingness to pay - Costs
(Area between the demand curve and the supply curve)
Total surplus
Total surplus
Total surplus of a competitive market
Q P
S
D Q*
Efficiency and competitive equilibrium
• An allocation of resources is efficient if it maximizes total surplus.
• First Welfare Theorem: A competitive
equilibrium generates an efficient allocation of resources.
Efficiency of equilibrium production
Q
0
P
S
D Q1 Q*
Total surplus decreases when production is
smaller than in the
competitive equilibrium.
Q
0
P
S
D Q* Q2
Negative surplus
Efficiency of equilibrium production
Total surplus decreases when production is
larger than in the
competitive equilibrium.
Q
0
P
S
D Q*
The area between supply and demand is
maximized when Q=Q*
Efficiency of equilibrium production
Finish Lecture 12
• Market supply
• Competitive equilibrium
• Total surplus and efficiency
• Taxes and subsidies
• Price maintenance
• Application: Imports
Competitive Markets
Taxes
• Consider a unit tax of t euros for each unit sold.
• Price payed by buyers, PB
• Price received by sellers, PS
PS = PB - t
D S
Effect of a unit tax
Q P
P*
Q*
Qt PS
PB
t
In equilibrium: S(PS) = S(PB-t) = D(PB)
Effect of a unit tax
• Output decreases: (Qt < Q* )
• Price payed by buyers increases (PB > P* )
• Price received by sellers decreases (PS < P* )
D S
D A
C
Who wins or looses with the tax?
Q P
P*
Q*
Qt PS
PB t
-Buyers: loose A+B -Sellers: loose D+C
-Government: Income A+D =t Qt
Unrecoverable welfare loss: B+C
B
The losses depend on elasticities
Q Q
P P
S
D S
D
Q*
P* P*
Qt Q*
PB
PS
t
Qt
PB
PS
t
Elastic supply, inelastic demand:
Buyers carry most part of the burden.
Inelastic supply, elastic demand:
Sellers carry most part of the burden.
Subsidies
• Consider a subsidy of s euros for each unit sold.
• Price payed by buyers PB
• Price payed by sellers, PS
PS = PB + s
Subsidy = negative tax
Subsidies
D S
Q P
P*
Q* Qs PB
PS
s
In equilibrium:
S(PS) = S(PB+s) = D(PB)
Subsidies
• Quantity sold increases (Qs > Q* )
• Price payed by buyers decreases (PC < P* )
• Price charged by sellers increases (PV > P* )
Wo gains, who looses?
-Buyers: gain C+D -Sellers: gain A+B
-State: pays A+B+C+D+E = s Qs Welfare loss: E
D S
Q P
P*
Q* Qs PB
PS
D s
C A B
E
The welfare loss depends on the elaticities
For small elasticities the welfare loss is smaller.
D1 S1
Q P
s
S2
s
D2
Example
• Suppose the supply of a competitive industry is given by P = 4 + 0.01Q and demand is given by P = 10 - 0.05Q.
• Calculate equilibrium price P* and production Q*.
• Suppose that the state imposes a tax of 1.2 for each unit sold.
• Calculate equilibrium production Qt. Which price PV* is received by the sellers and which price PC* is paid by the buyers?
• Calculate the losses of buyers and sellers and the tax revenue of the state. What is the welfare loss?
Example
• S(P) = 100P - 400; D(P) = 200 - 20P
• S(P*) = D(P*) → P* = 5, Q* = 100
• With tax: S(PS) = S(PB-t) = 100PB - 520, D(PB) = 200 - 20PB
• S(PB*-t) = D(PB*) → PB* = 6 → PS* = 4.8 Qt = 80
Example
• Consumer surplus:
Before = 0.5(10 - 5)100 = 250 After = 0.5(10 - 6)80 = 160
• Producer surplus:
Before = 0.5(5 - 4)100 = 50 After = 0.5(4.8 - 4)80 = 32
• Tax revenue: 1.2 · 80 = 96
• Welfare loss: 108 - 96 = 12
• Market supply
• Competitive equilibrium
• Total surplus and efficiency
• Taxes and subsidies
• Price maintenance
• Application: Imports
Competitive Markets
Price maintenance
• In some markets the state might want to maintain a price which is larger than the competitive equilibrium price (Example:
Labor market)
• There are different ways to implement this objective:
– Minimum prices
– Quantity restrictions – State purchases
Minimum prices
The state imposes a minimum price Pmin larger than the market price P*
Q P
S
D P*
Q*
Pmin
Q1 Q2
Excess supply
Example:
Minimum wage
Minimum prices
• Quantity sold decreases (Q1 < Q*)
• Price increases (Pmin > P*)
• There exists excess supply
A
Who gains, who looses?
Buyers: loose A+B
Sellers: gain A but loose C Welfare loss: B+C
C
Q P
S
D P*
Q*
Pmin
Q1
B
Quantity restrictions
Q P
D P*
Q*
PM S
SR
Q1
In order to maintain a price PM larger than the equilibrium price P* the state can restrict total output to Q1
Example: Oil
production regulated by OPEC.
• Quantity sold decreases (Q1 < Q*)
• Price increases (PM > P*)
• There is no excess supply
Quantity restrictions
Who gains, who looses?
Buyers: loose A+B
Sellers: gain A but loose C Welfare loss: B+C
Q P
D P*
Q*
PM S
SR
Q1
C B A
D + De Qe
State purchases
Q P
S
D P*
Q*
PM
Q2 Q1
In order to maintain a price PM larger than the equilibrium price P* the state has to buy a quantity Qe
• Quantity sold increases (Q2 > Q*)
• Quantity purchased by consumers decreases (Q1 < Q*)
• Price increases (PM > P*)
• There is no excess supply
State purchases
Who gains, who looses?
Buyers: loose A+B Sellers: gain A+B+C State: spends PM Qe Welfare loss: PMQe - C
D + De Qe
Q P
S
D P*
Q*
PM
Q2 Q1
B A C
Example
• Suppose the supply of a competitive industry is
given by P = (Q+2) / 3 and demand is given by P = (8 - Q) / 2.
• Calculate equilibrium price P* and production Q*.
• Suppose that the state wants to increase the
equilibrium price by 1. Calculate the state purchase Qe neccessary for this change.
• Calculate the losses of the buyers and the gains of the sellers.
• How big is the welfare loss?
Example
• S(P) = 3P-2; D(P) = 8-2P
• S(P*) = D(P*) → P* = 2, Q* = 4
• S(PM) = D(PM) + Qe → Qe = 5; QM = 7
Example
• Consumer surplus:
Before = 0.5(4-2)4 = 4 After = 0.5(4-3)2 = 1
• Producer surplus:
Before = 0.5(2-2/3)4 = 16/6 After = 0.5(3-2/3)7 = 49/6
• State expenses: 3·5 = 15
• Welfare loss:
3 - 33/6 +15 = 75/6
• Market supply
• Competitive equilibrium
• Total surplus and efficiency
• Taxes and subsidies
• Price maintenance
• Application: Imports
Competitive Markets
QS QB Pi
Imports
Q P
D P*
Q*
S (national supply)
Suppose that by opening itself to international trade a country can import a good at the international price Pi < P*.
Application: Imports
• Quantitity sold by national sellers decreases (QS < Q* )
• Quantity purchased increases (QB > Q*)
• Price decreases (Pi < P* )
The effect of allowing for imports
Who gains and who looses from allowing for imports?
Buyers: gain A+B+C Sellers: loose A
Welfare gain: B+C
QS QB
Pi
Imports
Q P
D P*
Q*
S (national supply)
A B C
• Most countries protect their industries by limiting the amount of imports by use of:
• Tariffs (import tax)
• Quotas (quantity restriction on imports)
Tariffs and quotas
QS QB Pi
Tariffs
Q P
D
A tariff increases the price of imports to: Pi + t
Pi + t
Imports
S
The effects of a tariff
• Quantity sold by national producers increases
• Quantity purchased decreases
• Imports decrease
• Price increases
QS QB Pi
Who gains, who looses?
Q P
D S
Pi + t
Import.
Buyers: loose A+B+C+D National producers: gain A State: gains C = t (QB-QS ) Welfare loss: B+D
A B C D
QS QB Pi
Quotas
Q P
D S
A quota restricts imports to be less
than some maximum amount I.
P
Import.
I
The effects of a quota
• Quantity sold by national producers increases
• Quantity purchased decreases
• Imports decrease
• Price increases
Who gains, who looses?
Buyers: loose A+B+C+D National producers: gain A
External producers: gain C Welfare loss: B+D
QS QB Pi
Q P
D S
P
Import.
A B C D
I
Finish Lecture 13 and 14
